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AE_Tutorial 12_Oscillators

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Tutorial 12 gives the design problems on Audio & Radio Frequency Oscillators.

AE_Tutorial 12. Problems on OSCILLATORS

Problems have been taken from:

“Microelectronic Circuit Design” by R.C.Jaeger and T.N. Blalock, 2nd Edition, McGraw Hill,2006.

“Microelectronic Circuits- Analysis & Design”, Muhammad H. Rashid, Thomson, Indian Edition, 1999.

Problem (1)Wien Bridge Oscillator

Figure 1
Figure 1 (Picture 1.png)
Figure 2
Figure 2 (graphics1.png)
Figure 3
Figure 3 (graphics2.png)

This is called Diode amplitude stabilization of a Wien Bridge Oscillator.

Determine frequency of oscillation & the amplitude of the oscillation.

[Ans:- 9.95 kHz,3.0V]

When the diodes are off,the gain of the amplifier is

Figure 4
Figure 4 (graphics3.png)

So that loop gain >1 and the oscillations grow.

When diode turn ON, the gain is

Figure 5
Figure 5 (graphics4.png)
and the oscillations decay.

PROBLEM(2)

Figure 6
Figure 6 (Picture 2.png)
Figure 7
Figure 7 (graphics5.png)

Design the Colpitt’s for oscillation frequency

Figure 8
Figure 8 (graphics6.png)

Step(1) Choose

Figure 9
Figure 9 (graphics7.png)

Figure 10
Figure 10 (graphics8.png)

Step(2) Calculate L from

Figure 11
Figure 11 (graphics9.png)

Figure 12
Figure 12 (graphics10.png)

Step(3) Calculate RF & RL.

Let RL=100kΩ Therefore RF=

Figure 13
Figure 13 (graphics11.png)

Step(4) Determine R1______Let A=10

Figure 14
Figure 14 (graphics12.png)

Figure 15
Figure 15 (graphics13.png)

Step(5) Determmine gm

Figure 16
Figure 16 (graphics14.png)
Figure 17
Figure 17 (graphics15.png)
Figure 18
Figure 18 (graphics16.png)

PROBLEM(3) Colpitts Oscillator Using BJT

Figure 19
Figure 19 (Picture 3.png)
Figure 20
Figure 20 (graphics17.png)

Calculate (i) Frequency of oscillation.

(ii)Check the Barkhausen criteria.

(iii)Determine R2.

Solution:-

RFC acts as a open circuit And CB and CE acts as a short circuit.

Therefore the Equivalent Circuit is :-

Figure 21
Figure 21 (Picture 4.png)
Figure 22
Figure 22 (Picture 5.png)

From the nodal equations we get equating the imaginary parts

Figure 23
Figure 23 (graphics18.png)

Equating Real parts we get

Figure 24
Figure 24 (graphics19.png)

For large values of

Figure 25
Figure 25 (graphics20.png)

Figure 26
Figure 26 (graphics21.png)

Gain

Figure 27
Figure 27 (graphics22.png)

Subs

Figure 28
Figure 28 (graphics23.png)
in Eq(2)

Figure 29
Figure 29 (graphics24.png)

For

Figure 30
Figure 30 (graphics25.png)

Figure 31
Figure 31 (graphics26.png)

Sub (4) in (3)

Figure 32
Figure 32 (graphics27.png)
Figure 33
Figure 33 (graphics28.png)

(i)This

Figure 34
Figure 34 (graphics29.png)
can be provided by BJT hence Barkhausen Criteria is satisfied

(ii)Frequency of oscillation=

Figure 35
Figure 35 (graphics30.png)

(iii)

Figure 36
Figure 36 (graphics31.png)

Figure 37
Figure 37 (graphics32.png)
Figure 38
Figure 38 (graphics33.png)

PROBLEM(4)LC-Tuned MOS Oscillator

Design an oscillator at

Figure 39
Figure 39 (graphics34.png)

Figure 40
Figure 40 (Picture 6.png)
Figure 41
Figure 41 (Picture 7.png)

Figure 42
Figure 42 (graphics35.png)

Figure 43
Figure 43 (graphics36.png)
Figure 44
Figure 44 (graphics37.png)
Figure 45
Figure 45 (graphics38.png)

For oscillation Loop Gain= 1∠0˚

Figure 46
Figure 46 (graphics39.png)
Figure 47
Figure 47 (graphics40.png)
Figure 48
Figure 48 (graphics41.png)
Figure 49
Figure 49 (graphics42.png)

Step(1) Choose a suitable value of C:

Let C=0.01μF

Step(2) Calculate the value of L from

Figure 50
Figure 50 (graphics43.png)

Figure 51
Figure 51 (graphics44.png)

Step(3) Find the value of R1 from Eq

Figure 52
Figure 52 (graphics45.png)

Figure 53
Figure 53 (graphics46.png)

Step(4)

Figure 54
Figure 54 (graphics47.png)

Figure 55
Figure 55 (graphics48.png)

PROBLEM(5)

Design a Hartley Oscillator at fo=5MHz.USE 2N3822 n-JFET whose parameters are

Figure 56
Figure 56 (graphics49.png)

Load Resistance is RL=100Ω

The circuit is:-

Figure 57
Figure 57 (Picture 8.png)

Practically it is implemented in the following manner:-

Figure 58
Figure 58 (Picture 11.png)

The incremental circuit is given in Figure 10.

Figure 59
Figure 59 (Picture 10.png)

Solution:-

Figure 60
Figure 60 (graphics50.png)

Figure 61
Figure 61 (graphics51.png)

BY analysis:-

Figure 62
Figure 62 (graphics52.png)

We take

Figure 63
Figure 63 (graphics53.png)

Figure 64
Figure 64 (graphics54.png)
Figure 65
Figure 65 (graphics55.png)
Figure 66
Figure 66 (graphics56.png)

PROBLEM(6)CRYSTAL OSCILLATOR

Figure 67
Figure 67 (Picture 12.png)

This is a Colpitts-derived op-amp crystal oscillator which uses crystal as an inductor.

This uses a 2 MHz crystal oscillator

Figure 68
Figure 68 (graphics57.png)

Find the frequency of oscillator.

Given

Figure 69
Figure 69 (graphics58.png)

Figure 70
Figure 70 (Picture 13.png)
Figure 71
Figure 71 (graphics59.png)

Equivalent Circuit of Crystal Oscillator:

Figure 72
Figure 72 (Picture 14.png)

This can also be expressed as:

Figure 73
Figure 73 (Picture 15.png)
Figure 74
Figure 74 (graphics60.png)

Effective Capacitance Ceq is parallel with

Figure 75
Figure 75 (graphics61.png)
is given by

Figure 76
Figure 76 (graphics62.png)
Figure 77
Figure 77 (graphics63.png)

It is given that 2MHz crystal is used. Hence the result is self consistent.

This is the frequency of the Crystal Oscillator.

Figure 78
Figure 78 (graphics64.png)

Figure 79
Figure 79 (graphics65.png)

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